How can transformations help in reducing skewness in a dataset?
- They can make the distribution more symmetric
- They can shift the mean towards the skew
- They can shift the mode towards the skew
- Transformations cannot reduce skewness
Transformations, such as logarithmic or square root transformations, can help in reducing skewness by making the distribution more symmetric. The choice of transformation often depends on the degree and direction of skewness.
How does the standard deviation affect the shape of a normal distribution?
- Changes the kurtosis
- Changes the skewness
- Changes the spread or dispersion
- Does not affect the shape
The standard deviation, a measure of dispersion or spread, determines the width of a normal distribution. A larger standard deviation results in a wider, flatter distribution, while a smaller standard deviation results in a narrower, steeper distribution.
A _______ t-test is used to compare two related samples or repeated measurements on a single sample.
- Independent
- One-sample
- Paired
- Two-sample
A Paired t-test is used to compare two related samples or repeated measurements on a single sample. It's often used in before-and-after scenarios where the same individuals are measured twice.
What is a random variable in probability theory?
- A factor that doesn't change
- A variable that can take on different values, each with an associated probability
- An unknown variable
- An unpredictable factor
A random variable in probability theory is a variable that can take on different values, each with an associated probability. It's not "random" in the everyday sense of the word, but its exact value is uncertain until it's observed.
The _________ test is a non-parametric test that compares the medians of two paired groups.
- Chi-square
- Mann-Whitney U
- Sign
- Wilcoxon Signed Rank
The Wilcoxon Signed Rank test is a non-parametric test that compares the medians of two paired groups.
Why is interval estimation generally preferred over point estimation?
- Because it gives more accurate results
- Because it is easier to calculate
- Because it is less affected by outliers
- Because it provides a range of possible values rather than a single point
Interval estimation is generally preferred over point estimation because it provides a range of possible values rather than a single value. This range of values gives a better understanding of the uncertainty around the estimate, hence, it provides more information than a single point estimate.
Spearman's Rank Correlation is especially useful when the relationship between variables is ________, but not necessarily linear.
- Bimodal
- Monotonic
- Negative
- Positive
Spearman's Rank Correlation is especially useful when the relationship between variables is monotonic, but not necessarily linear. A monotonic relationship is one where the variables tend to change together, but not necessarily at a constant rate.
How is the test statistic computed in the Sign Test?
- By averaging the ranks
- By counting the number of positive and negative signs
- By summing the differences
- By summing the ranks
In the Sign Test, the test statistic is computed by counting the number of positive and negative signs of the differences between paired observations.
In a box plot, the 'box' represents the ________ quartile range of the data.
- Full
- Inter
- Lower
- Upper
The 'box' in a box plot represents the interquartile range (IQR) of the data. This is the range within which the middle 50% of the data falls, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
The distribution of the sample mean will approach a normal distribution as the sample size increases, according to the _________.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
According to the Central Limit Theorem, the distribution of the sample mean will approach a normal distribution as the sample size increases. Regardless of the shape of the population, the distribution of sample means taken with large enough sample size can be approximated by a normal distribution.